Question

Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b): b = a + 1} is reflexive, symmetric and transitive.

Answer 1

(i) R is not reflexive : a ≠ a + 1.

(ii) R is not symmetric : If b = a + 1, then a ≠ b + 1.

(iii) R is not transitive :If b = a + 1, c = b + 1, then c ≠ a + 1.